(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find V_{L}(t) and V_{c}(t) in the circuit below

Where V_{s}= cos(200[itex]\pi[/itex]t) V

2. Relevant equations

[itex]\alpha[/itex] = [itex]\frac{1}{2RC}[/itex]

ω_{0}= [itex]\frac{1}{\sqrt{LC}}[/itex]

[itex]\omega[/itex]_{0}= [itex]\sqrt{\omega^{2}-\alpha^{2}}[/itex]

3. The attempt at a solution

Well, I found the total capacitance

C = 1.5 uF

Then, I found [itex]\alpha[/itex]:

[itex]\alpha[/itex] = [itex]\frac{1}{2(100Ω)(1.5uF)}[/itex] ≈ 3333 s^{-1}

and

ω_{0}= [itex]\frac{1}{\sqrt{(20mH)(1.5uF)}}[/itex] ≈ 5774 s^{-1}

So V_{c}= B_{1}e^{-3333}cos([itex]5774\pi[/itex]t) + B_{2}e^{-3333}sin([itex]5774\pi[/itex]t)

That's as far as I went. I have no idea what I'm doing :|. Also, please note that I have NOT had differential equations. This class does not require it, so please give an answer without using DQ's.

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# Homework Help: RLC Circuit total capacitance

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